Problem: Simplify the following expression: $\sqrt{44} + \sqrt{99}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{44} + \sqrt{99}$ $= \sqrt{4 \cdot 11} + \sqrt{9 \cdot 11}$ Separate the radicals and simplify. $= \sqrt{4} \cdot \sqrt{11} + \sqrt{9} \cdot \sqrt{11}$ $= 2\sqrt{11} + 3\sqrt{11}$ Finally, simplify by combining the terms. $= ( 2 + 3 )\sqrt{11} = 5\sqrt{11}$